Top-seeded Amelie Mauresmo beat Marion Bartoli 6-0, 6-2, while former No. 1 Martina Hingis topped third-seeded Francesca Schiavone 6-1, 6-1 to reach the quarterfinals of the Qatar Open on Wednesday.
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Mauresmo, who is ranked No. 2, broke her fellow Frenchwoman three times in the first set.
"I am happy with the way I played today," Mauresmo said. "It wasn't a difficult match. I am fairly relaxed these days and I am enjoying the level of tennis I play nowadays."
Second-seeded Nadia Petrova beat Eleni Daniilidou of Greece 6-1, 6-2. The Russian will now play in the quarters Li Na, who upset fifth-seeded Daniela Hantuchova 4-6, 7-6 (7/5), 6-1.
Also, Ai Sugiyama of Japan saved two match points to upset fourth-seeded Anastasia Myskina of Russia 7-6 (7/2), 6-7 (6/8), 6-4 to move into the final eight.
Sugiyama won in 2 hours, 50 minutes over the 2003 and 2004 Qatar champion.
In other second-round matches, sixth-seeded Svetlana Kuznestova beat fellow Russian Maria Kirilenko 6-4, 7-6 (7/4); and Italy's Roberta Vinci defeated Maria-Vento Kabchi of Venezuela 6-2, 6-3.